Thermodynamics of spin S=1/2 antiferromagnetic uniform and alternating-exchange Heisenberg chains
- Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)
- Max-Planck-Institut fuer Festkoerperforschung, Heisenbergstrasse 1, Postfach 800665, D-70569 Stuttgart, (Germany)
- Institute for Solid State Physics, University of Tokyo, Roppongi 7-22-1, Tokyo 106, (Japan)
- Institut Romand de Recherche Numerique en Physique des Materiaux, IN-Ecublens, CH-1015 Lausanne, (Switzerland)
- Universitaet zu Koeln, Institut fuer Theoretische Physik, Zuelpicher Strasse 77, D-50937, (Germany)
The magnetic susceptibility {chi}{sup *}(t) and specific heat C(t) versus temperature t of the spin S=1/2 antiferromagnetic (AF) alternating-exchange (J{sub 1} and J{sub 2}) Heisenberg chain are studied for the entire range 0{<=}{alpha}{<=}1 of the alternation parameter {alpha}{identical_to}J{sub 2}/J{sub 1} (J{sub 1}, J{sub 2}{>=}0, J{sub 2}{<=}J{sub 1}, t=k{sub B}T/J{sub 1}, {chi}{sup *}={chi}J{sub 1}/Ng{sup 2}{mu}{sub B}{sup 2}). For the uniform chain ({alpha}=1), the high-accuracy {chi}{sup *}(t) and C(t) Bethe ansatz data of Kluemper and Johnston (unpublished) are shown to agree very well at low t with the respective exact theoretical low-t logarithmic correction predictions of Lukyanov [Nucl. Phys. B 522, 533 (1998)]. Accurate ({approx}10{sup -7}) independent empirical fits to the respective data are obtained over t ranges spanning 25 orders of magnitude, 5x10{sup -25}{<=}t{<=}5, which contain extrapolations to the respective exact t=0 limits. The infinite temperature entropy calculated using our C(t) fit function is within 8 parts in 10{sup 8} of the exact value ln 2. Quantum Monte Carlo (QMC) simulations and transfer-matrix density-matrix renormalization group (TMRG) calculations of {chi}{sup *}({alpha},t) are presented for 0.002{<=}t{<=}10 and 0.05{<=}{alpha}{<=}1, and an accurate (2x10{sup -4}) two-dimensional ({alpha},t) fit to the combined data is obtained for 0.01{<=}t{<=}10 and 0{<=}{alpha}{<=}1. From the low-t TMRG data, the spin gap {delta}({alpha}) is extracted for 0.8{<=}{alpha}{<=}0.995 and compared with previous results, and a fit function is formulated for 0{<=}{alpha}{<=}1 by combining these data with literature data. We infer from our data that the asymptotic critical regime near the uniform chain limit is only entered for {alpha}(greater-or-similar sign)0.99. We examine in detail the theoretical predictions of Bulaevskii [Sov. Phys. Solid State 11, 921 (1969)], for {chi}{sup *}({alpha},t) and compare them with our results. To illustrate the application and utility of our theoretical results, we model our experimental {chi}(T) and specific heat C{sub p}(T) data for NaV{sub 2}O{sub 5} single crystals in detail. The {chi}(T) data above the spin dimerization temperature T{sub c}{approx_equal}34 K are not in quantitative agreement with the prediction for the S=1/2 uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. Fitting the {chi}(T) data using our {chi}{sup *}({alpha},t) fit function, we obtain the sample-dependent spin gap and range {delta}(T=0)/k{sub B}=103(2) K, alternation parameter {delta}(0)(ident to)(1-{alpha})/(1+{alpha})=0.034(6) and average exchange constant J(0)/k{sub B}=640(80) K. The {delta}(T) and {delta}(T) are derived from the data. A spin pseudogap with magnitude {approx_equal}0.4{delta}(0) is consistently found just above T{sub c}, which decreases with increasing temperature. From our C{sub p}(T) measurements on two crystals, we infer that the magnetic specific heat at low temperatures T(less-or-similar sign)15 K is too small to be resolved experimentally, and that the spin entropy at T{sub c} is too small to account for the entropy of the transition. A quantitative analysis indicates that at T{sub c}, at least 77% of the entropy change due to the transition at T{sub c} and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom. (c) 2000 The American Physical Society.
- OSTI ID:
- 20215836
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 61, Issue 14; Other Information: PBD: 1 Apr 2000; ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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